The problem of the invariance of dimension in the growth of modern topology,part II

Summary This work examines the historical origins of topological dimension theory with special reference to the problem of the invariance of dimension. Part I, comprising chapters 1–4, concerns problems and ideas about dimension from ancient times to about 1900. Chapter 1 deals with ancient Greek ideas about dimension and the origins of theories of hyperspaces and higher-dimensional geometries relating to the subsequent development of dimension theory. Chapter 2 treatsCantor's surprising discovery that continua of different dimension numbers can be put into one-one correspondence and his discussion withDedekind concerning the discovery. The problem of the invariance of dimension originates with this discovery. Chapter 3 deals with the early efforts of 1878–1879 to prove the invariance of dimension. Chapter 4 sketches the rise of point set topology with reference to the problem of proving dimensional invariance and the development of dimension theory. Part II, comprising chapters 5–8, concerns the development of dimension theory during the early part of the twentieth century. Chapter 5 deals with new approaches to the concept of dimension and the problem of dimensional invariance. Chapter 6 analyses the origins ofBrouwer's interest in topology and his breakthrough to the first general proof of the invariance of dimension. Chapter 7 treatsLebesgue's ideas about dimension and the invariance problem and the dispute that arose betweenBrouwer andLebesgue which led toBrouwer's further work on topology and dimension. Chapter 8 offers glimpses of the development of dimension theory afterBrouwer, especially the development of the dimension theory ofUrysohn andMenger during the twenties. Chapter 8 ends with some concluding remarks about the entire history covered. Dedicated to Hans Freudenthal     

Gauss's geodesy and the axiom of parallels

It is a myth that Gauss measured a certain large triangle specifically to determine its angle sum; he did so in order to link his triangulation of Hanover with contiguous ones. The sum of the angles differed from 180° by less than two thirds of a second; he is known to have mentioned in conversation that this constituted an approximate verification of the axiom of parallels (which he regarded as an empirical matter because his studies of hyperbolic trigonometry had led him to recognize the possibility of logical alternatives to Kant and Euclid). However, he never doubted Euclidean geometry in his geodetic work. On the contrary, he continually used 180° angle sums as a powerful check for observational errors, which helped him to achieve standards of precision equivalent to today's. Nor did he ever plan an empirical investigation of the geometrical structure of space.     

Aristotele e l'incommensurabilità

Riassunto Aristotele accenna a due diverse dimostrazioni della incommensurabilità tra lato e diagonale di uno stesso quadrato, una esatta e l'altra, avverte, errata. Nel presente lavoro viene presa in esame quest'ultima proponendone una ricostruzione in connessione, come é accennato da Aristotele, con le argomentazioni di Zenone.Nel corso del lavoro vengono esaminati due altri brani di Aristotele attraverso i quali é possibile osservare un momento dello sviluppo matematico dell'algoritmo euclideo e il cosiddetto postulato di Eudosso-Archimede nel più vasto ambito dei primi contatti con problemi di analisi infinitesimale.Nell'Appendice, poi, vengono elencati tutti i brani di Aristotele raccolti dall'autore sulla detta incommensurabilità.

---

Summary Aristotle mentions two different demonstrations of the incommensurability of side with diagonal of the same square, one of which is correct, and the other, as he points out, incorrect. This work examines the latter suggesting a reconstruction of it in connection, as Aristotle mentioned, with Zeno's argumentations.In the course of this work, two other passages by Aristotle are examined, by which it is possible to observe a moment of the mathematical development of the Euclidean algorithm and the so called Axiom of Eudoxus-Archimedes in the broader ambit of early contacts with problems of infinitesimal analysis.In the Appendix, secondly, all the passages by Aristotle regarding incommensurability gathered by the author are listed.

---

Résumé Aristote parle de deux différentes démonstrations de l'incommensurabilité entre le côté et la diagonale d'un même carré, une exacte et l'autre, nous prévient-il, inexacte. Dans ce travail on examine cette dernière démonstration en connexion, comme Aristote lui-même le suggère, avec les argumentations de Zénon.Au cours du travail l'auteur examine deux autres morceaux d'Aristote, à travers lesquels il est possible d'observer un moment du développement mathématique de l'algorithme euclidien et ce qu'on appelle le postulat d'Eudoxe-Archimède dans le domaine bien plus vaste des premiers contacts avec des problèmes d'analyse infinitésimale.Dans l'appendice on peut trouver la liste de tous les morceaux d'Aristote que l'auteur a rassemblés sur la susdite incommensurabilité.

---

---

Memoria presentata da C. Truesdell     

“... in Christophorum Clavium de Contactu Linearum Apologia” Considerazioni attorno alla polemica fra Peletier e Clavio circa l'angolo di contatto (1579–1589)

Summary In this work 1 focus my attention upon the question of the angle of tangency in the XVI^th Century, especially in the polemic between J. Peletier and Chr. Clavius (1579–1589). The interest in the question favored deliberation about the theory of proportions, the principle of Eudoxus-Archimedes and the set of angles of tangency (this is a non-Archimedian set); there were problems about logical proofs and geometrical proofs.

---

---

Memoria presentata da H. Freudenthal     

Die anorganischen Bestandteile des Honigtaues vonMegoura viciae Buckt

Summary In the honeydew ofMegoura viciae Buckt., sucking on the sieve tube sap ofVicia faba, the following cations are present in measurable quantities: potassium (13.0–14.1 mg/ml), sodium (0.04–0.051 mg/ml), magnesium (1.8–2.3 mg/ml) and calcium (0.07–0.09 mg/ml). There are only traces of copper, iron, manganese, zinc, cobalt and molybdenum. Amongst the anions, phosphate was found at 1.9–2.5 and chloride at 0.02–0.05 mg/ml, whereas nitrate and sulphate could not be detected.     

Sur l'action de l'acide 2,4-dichlorophénoxyacétique sur la croissance des racines deZea mays et dePisum cultivéesin vitro

Summary (1) A response ofZea mays andPisum roots cultured aseptically to 2,4-dichlorophenoxyacetic acid has been observed.Depending on the concentrationZea mays shows an increase of the growth rate (optimal concentration 10^–11 mol) which turns over to an inhibition (above 10^–7 mol). The curve is similar to that obtained by 3-indoleacetic acid, which proves the phytohormonal character of 2,4-D.(2) ThePisum root is more sensitive than theZea mays root. A concentration of 10^–7 molinhibitsPisum in a high degree, whileZea mays is no more inhibited, thus demonstrating the selective herbicidal action of 2,4-D against isolated roots of Dicotyledons culturedin vitro.     

Steroid stereochemistry

Zusammenfassung Ein Überblick über die angewandten Methoden zur Bestimmung der absoluten Konfiguration in Steroidseitenketten wurde gegeben. Die allgemeine Anwendung derR- undS-Regel wurde empfohlen.

---

---

In part, a summary of recommendations presented by the author to a National Academy of Sciences and National Research Councilad hoc Committee on Steroid Nomenclature (R. C. Elderfield, Chairman); October 13–15, 1961, Columbus (Ohio). The meeting of thead hoc committee was made possible by a grant from the U.S. Air Force Office of Scientific Research.

---

Part XV of a series entitledSteroid and Related Natural Products. Refer toG. R. Pettit andP. Hofer, Exper.19, 67 (1963), for the preceding contribution.     

Newton and the classical theory of probability

Summary Probabilistic ideas and methods from Newton's writings are discussed in § 1: Newton's ideas pertaining to the definition of probability, his probabilistic method in chronology, his probabilistic ideas and method in the theory of errors and his probabilistic reasonings on the system of the world. Newton's predecessors and his influence upon subsequent scholars are dealt with in §2: beginning with his predecessors the discussion continues with his contemporaries Arbuthnot and De Moiver, then Bentley. The section ends with Laplace, whose determinism is seen as a development of the Newtonian determinism.An addendum is devoted to Lambert's reasoning on randomness and to the influence of Darwin on statistics. A synopsis is attached at the end of the article.Abbreviations PT abridged Philosophical Transactions of the Royal Society 1665–1800 abridged. London, 1809 - Todhunter I. Todhunter, History of the mathematical theory of probability, Cambridge, 1865 To the memory of my mother, Sophia Sheynin (1900–1970)     

Geometrical constructions equivalent to non-linear algebraic transformations of the plane in Newton's early papers

Summary The theory of constructive formation of plane algebraic curves in Newton's writings is discussed in § 1: the apparatus by which Newton forms the curves, Newton's theorems on forming unicursal curves, his theory of conics, and his theory of (m, n) correspondence. Special Cremona plane and space transformations obtained by Newton's organic method are dealt with in § 2. The article ends with § 3, which shows two different directions in the theory of the constructive formation of plane algebraic curves in the XVIII-XIXth centuries. A synopsis is appended.Abbreviations MPN The Mathematical Papers of Isaac Newton, edited by D. T. Whiteside, Vols. 1–3, Cambridge, 1967–1969 - Hudson H. Hudson, Cremona Transformations in Plane and Space, Cambridge, 1927 - PT (abridged) Philosophical Transactions of the Royal Society 1665–1800 (abridged), London, 1809 - Andreev ₁ K. A. Andreev, On geometrical correspondences ... (in Russian), Moscow, 1879 - Andreev ₂ K. A. Andreev, On the Geometrical Formation of Plane Curves (in Russian), Kharkov, 1875     

Alkaloid studies XXIII isolation of four new aspidosperma alkaloids: Cylindrocarpine,refractine, pyrifoline,and pyrifolidine

Zusammenfassung Die Isolierung von vier neuenAspidosperma-Alkaloiden ergabCylindrocarpin (erstes N-Cinnamoyl-dihydroindolderivat) sowieRefractin, Pyrifolin undPyrifolidin (alles N-Acetyl-dihydroindole), die alle vier eine Methoxylgruppe im Dihydroindolsystem besitzen.

---

---

Postdoctorate research fellow 1958–1959 (Wayne State University); 1959–1960 (Stanford University).

---

Paper XXII,J. S. E. Holker, M. Cais, F. A. Hochstein undC. Djerassi, J. org. Chem.24, 314 (1959).     

Influence of cyclic nucleotides on protein synthesis in vascular smooth muscle

Summary The incorporation of leucice-¹⁴C into protein in bovine mesenteric arteries was augmented by cyclic GMP (10^–3 M) and decreased by cyclic AMP (10^–3 M). There was no effect of 5 AMP (10^–3 M). The phosphodiesterase inhibiting drugs theophylline (10^–3 M) and papaverine (5×10^–5 g/ml) both decreased the leucine-¹⁴C incorporation.We are indebted to Mrs.Lena Burlin for hear assistance. Finacial support has been provided by the Swedish State Medical Research Council (No. 04X-101X-4498).     

Effects of three synthetic peptides analogous to neurohypophyseal hormones on the excitability of giant neurones ofAchatina fulica Férussac

Summary Deamino-dicarba-(d-d-)oxytocin andd-d-Arg-vasotocin at 10^–4 kg/l showed an excitatory effect on the periodically oxcillating neurone (PON) ofAchatina fulica Férussac.d-d-Arg-vasopressin had no effect.     

Karyotypes of bats of the subfamily carolliinae (mammalia; phyllostomatidae) and their evolutionary implications

Zusammenfassung Es werden die Kennzeichen der Chromosomen vonRhinophylla fischeri, R. pumilio undCarollia castanea beschrieben. Für die GattungCarollia ist bei niedriger Diploidzahl (21 , 20 ) eine niedrige « nombre fondamental » (34–36) charakteristisch. Für die GattungRhinophylla wird eine grössere Diploidzahl (34–36) und eine grössere « nombre fondamental » (56–62) gefunden.

---

---

We thank Dr.C. J. Marinkelle andA. Cadena of the Universidad de Los Andes for assistance and facilities.Pvt. Genaro Lopez assisted with the field work. Dr.R. Strandtmann translated the summary. Supported by National Science Foundation Grant No. GB-8120.     

On the interaction of hypoxanthine with adenine

Résumé Une conversion non-enzymatique d'hypoxanthine en adénine fut proposée sur la base d'observations spectrophotométriques obtenues de solutions contenant adénine et hypoxanthine dans 1–5M de phosphate d'ammonium. Les résultats fournis par les expériences sur la radioactivité ne confirme pas la conclusion émise parBowne ² que hypoxanthine et adénine agissent l'une sur l'autre en solution concentrée de phosphate d'ammonium pour former de l'adénine.

---

---

This work was supported by United States Public Health Service Grants No. AM-08897, No. AM-10126, and No. 2A-5124; a grant from The Arthritis Foundation (Northern California Chapter); and from the Committee on Research, University of California School of Medicine (San Francisco).     

Die Synthese des Novobiocins

Summary The synthesis of the antibiotic novobiocin is described. First the essential carbohydrate, the 3-O-carbamoylnoviose was synthesized fromd-glucose. A number of steps (1–6) led to the 3,5,6-tri-O-benzyl-2-O-methyl-d-galactono--lactone (6) which is characterized by the correct array of carbon atoms inherent to the noviose. Further transformations (7–15) finally yielded the carbohydrate. The problem of glycosidation is discussed in some detail. Glycosidation of a suitable aglycon precursor (18) with 2,3-O-carbonyl--noviosyl-chloride (22) proved possible and led to the isolation of an-glycoside (23) which was further transformed (24–28) into novobiocin.

---

---

Chemische Forschungsabteilung der F. Hoffmann-La Roche & Co. AG, Basel.

---

Vortrag Dr.B. P. Vaterlaus, gehalten an der Gordon Research Conference on Steroids and other Natural Products, 16.–20. Juli 1962, New Hampton, N.H., USA, und vor der Basler Chemischen Gesellschaft, 8. November 1962. Im Auszug:H. Spiegelberg,Synthèse du 3-O-carbamoylnoviose, sucre de la novobiocine, Symposium international de chimie organique, Bruxelles, 15. Juni 1962;J. Kiss,The Synthesis of Noviose and Allied Compounds, Birkbeck College (Univ. London), 23. Oktober 1962. Der vorliegende Aufsatz ist Gegenstand von Detailpublikationen in den Helv. chim. Acta, in Vorbereitung (1963).     

Le chlore,oligo-élément indispensable pourLemna minor

Zusammenfassung Mit einer nachBroyer undStout gereinigten Nährlösung konnte nicht bewiesen werden, dass Cl^– ein fürLemna minor unentbehrliches Ion sei. Es wurde deshalb eine neue Reinigungsmethode ausgearbeitet, die eine Verminderung des Cl^–-Gehaltes der Nährlösung auf weniger als 10 µg/l erlaubt. In einer derart behandelten Nährlösung zeigtLemna minor folgende Mangelsymptome: Verschwinden der Wurzel, Chlorose und sehr starke Verkleinerung der Blätter. Beigabe von Cl^– zur Nährlösung genügt, um die Mangelsymptome zu verhüten oder sie zu kompensieren. Unter den angegebenen Bedingungen benötigtLemna minor ungefähr 100 µg Cl^–/l.     

Dissociation-constants of metal-ion-complexes with alkaline phosphatase from pig kidney

Summary Using metal-ion buffers it was possible to remove Zn²⁺, Mg²⁺ and Mn²⁺ ions of pig kidney alkaline phosphatase reversibly. The dissociation constants obtained are K_EMg:4·10^–7 M, K_EMn:4·10^–8 M and K_EZn:8·10^–13 M (22°C, pH:9.6, :0.07).Acknowledgement: The authors thank Dr.H. U. Wolf for helpful suggestions and valuable discussion and MissH. Köth for technical assistance.     

Cell wall degradation in senescing tobacco leaf discs

Zusammenfassung In ausgestanzten Blattstücken vonNicotiana tabacum, welche auf Wasser schwimmend inkubiert werden, findet im Verlauf von 7 Tagen ein beträchtlicher Abbau der Hemizellulose statt. Benzyladenin (10^–5 M) verzögert den Abbau, Abscisinsäure (5×10^–5 M) verstärkt ihn. Der Gehalt an Zellulose verändert sich im Verlauf der Alterung kaum.

---

---

The author is indebted to Dr.A. Artho and to theF. J. Burrus & Cie, Manufacture de Cigarettes, Boncourt, Switzerland, for generously supporting the present work. The skillful technical assistance of MissM. Schellenberg and the supply of abscisic acid by Hoffmann-La Roche, Basel, are gratefully acknowledged.     

Action de la capsicine sur la multiplication et la virulence de l'Agrobacterium tumefaciens

Summary It was established that the treatment of liquid cultures ofAgrobacterium tumefaciens with capsicine (in doses of 0.0025–0.01) in the course of 6 h, causes a more abundant and quicker multiplication of the micro-organism and an increase of its virulence, as measured by the method ofBernaerts andDe Ley.     

Spontaneous occurrence of aneuploidy in somatic cells ofRana tigrina (Ranidae: Anura)

Zusammenfassung Es wurde Aneuploidie bis zu drei Chromosomen in den männlichen Körperzellen vonRana tigrina (Ranidae: Anura: Amphibia) beobachtet. Die Variationen betreffen:2n–3, 2n–2, 2n–1, 2n, 2n+1, 2n+2 und2n+3.

---

---

Acknowledgments. My sincere thanks are due to Dr.S. P. Sharma, Zoology Department, for facilities; to Mr.R. K. Pillai and MissMadhu for technical assistance with preparations and Drs.K. K. Rishi andL. K. Vats for helpful suggestions.